ORIGINAL: Phaedrus-MMVI
Here's a twist. In general, if a public entity, like a Parks Department has a model facility on public land then they cannot require AMA membership. However, IF an AMA club LEASES land from the Parks Department, THEN the club can require AMA membership to be a member of the club (in fact they have to do so) and since they have a lease, they control who can access a site.
of course, if all the above is true, the land isn't any longer a park but merely leased public property.